Inverse Problems at RPI (IPRPI)

IPRPI Center research programs emphasize cross disciplinary inverse problems where (1) solutions have a significant impact on society, and advance scientific understanding; and (2) contribute to the education of young people who will join the scientific and engineering enterprise. The focus of inverse problems is to find objects and/ or their material or biological properties that cannot be directly measured. For these problems, application areas include geophysics and geotechnical work including earthquake dynamics, medical imaging that targets medical diagnosis, radar imaging including enhancing home security, and a broad set of problems in solid mechanics and electromagnetics. Applied mathematics and computation play a central role. This is a vast scientific area, in which Rensselaer has a significant, high quality, well established science and engineering base.

Among those problems addressed at Rensselaer, are some at the most basic scientific level, for example finding properties of the earth’s substructure from seismic measurements, or defining new experiments where the data yield new human tissue properties. Others are focused on direct applications, for example finding sediment properties of the seabed, establishing the integrity of dikes, locating objects concealed by vegetation cover, locating mines in the sea environment, finding malignant tumors in biological tissue, locating sources of heart malfunction, or finding temperature distributions in inaccessible regions. In all cases it is either not possible, as in determining the earth’s substructure properties, or not desirable, as in locating tumors in tissue, to make direct measurements. In all cases, solution of these problems results in improved quality and safer lives.

Scientific challenges include modeling of the physical problem, creation of new mathematics for analysis of the model, identification of appropriate (often large) and/ or rich data sets, scientific computing and visualization, and experimental verification. Approaches are based on effective use of a mathematical model in order to make optimal use of the data. Since inverse problems are concerned with the processing of data and extraction of relevant information, the field is a part of Computation and Information Technology. Each individual application may also be part of one additional thrust such as Bioengineering and Biotechnology (e.g. for tissue property identification), or the Energy and the Environment (e.g. establishing the integrity of dikes).

Rensselaer’s goal in creating this center is to create a synergistic group of researchers with complementary talents and related interests whose combined expertise can successfully solve an even wider group of important problems. Funding includes significant opportunity for postdoctoral fellows and graduate students who work in team environments to advance problem solutions.